Heres my problem.
Consider the group <R,+> (reals under addition) and its normal subgroups Z (integers) and Q (rationals0. (These are normal because R is abelian,
(i) Find an element of Q/Z of order 350.
(ii) Show that Q/Z is the torsion subgroup of R/Z. This problem is quite straightforward if you use the definitions and stay focussed; in
particular, pay attention to the definition of a rational number.
(iii) Show that R/Q is torsion free. Think carefully about the elements of R that are not in Q here.
Factor Groups and Torsion Groups are investigated. The solution is detailed and well presented.